Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Sparkles the Clown makes balloon animals for children at birthday parties. At Michelle's party, she made 5 balloon poodles and 1 balloon giraffe, which used a total of 13 balloons. For Tiana's party, she used 18 balloons to make 3 balloon poodles and 4 balloon giraffes. How many balloons does each animal require?

Answer 1

Let:

x = Balloons required for poodles

y = Balloons required for giraffes

so:

`\begin{gathered} 5x+y=13_{\text{ }}(1) \\ 3x+4y=18_{\text{ }}(2) \end{gathered}`

Using elimination method:

`\begin{gathered} 4(1)-(2) \\ 20x-3x+4y-4y=52-18 \\ 17x=34 \\ x=(34)/(17) \\ x=2 \end{gathered}`

Replace x into (1):

`\begin{gathered} 5(2)+y=13 \\ 10+y=13 \\ y=13-10 \\ y=3 \end{gathered}`

Answer:

x = 2

y = 3